Lecture on Multicollinearity

What is Multicollinearity?

• Occurs when two or more independent variables are strongly correlated.
• Causes issues in separating the effects of individual variables.
• In regression models, makes it difficult to determine coefficients (e.g., b1 and b2).
• Leads to instability in regression models.

Implications

• For predictions: Multicollinearity does not affect the quality of the prediction.
• For measuring variable influence: Coefficients cannot be interpreted meaningfully if multicollinearity is present.

Diagnosing Multicollinearity

• Examine if a variable (e.g., x1) is identical to or a combination of other variables.
• Set up a regression model with x1 as the dependent variable.
  • If x1 can be predicted well by other variables, it might be redundant.
• Repeat this process for all variables, creating k new regression models.

Key Metrics

• Tolerance:
  • Calculated as 1 - R² (coefficient of determination).
  • Multicollinearity may exist if tolerance < 0.1.
• Variance Inflation Factor (VIF):
  • Calculated as 1 / (1 - R²).
  • Multicollinearity may exist if VIF > 10.

Checking Multicollinearity Online

• Visit datadap.net and use the statistics calculator.
• Steps:
  • Clear table for new data or use example data.
  • Choose dependent and independent variables for regression.
  • Click "check conditions" for results.
  • Examine tests such as linearity, normality of errors, multicollinearity (tolerance and VIF), and homoscedasticity.

Further Learning

• Introduction to dummy variables will be covered in the next video.